There’s such an awareness of and a desire for glamour,” says Carleton Varney, who, as heir to the unparalleled decorator Dorothy Draper, is in a unique position to know. Hers is an imposing legacy, one that he’s more than lived up to in his long tenure as owner and president of Dorothy Draper & Company. “In over 40 years in the business, I’ve designed cruise ships, hotels, country clubs, resorts, you name it,” he says. How many designers can claim, as Varney does, to have designed a supermarket?

For all the diversity of these projects, the challenge inherent in each remains the same. “We can all make rooms pretty,” muses Varney. “But do we have an ability to create a look, a look that sustains itself?”

Running along most of the house’s rear elevation, the conservatory features such subtle Victorian-inspired details as mullioned transoms and Gothic Revival–style furniture. Mansour carpet. McGuire chairs and tables.

When it comes to a sprawling Norman-style house on Long Island, New York, the answer is a definite yes. Its owners raised their family in a smaller two-story residence nearby. After their children were grown, they, counterintuitively, “didn’t downsize; we upsized instead,” the wife says. Her husband, who’s frank about saying that, given a Depression-era childhood, he finds solace in possessions—lots of them—puts it succinctly: “I wanted bigger.”

The house they purchased was “a very bland, cottagey kind of thing,” according to architect Norman Wax, who, in an extensive renovation, transformed it entirely, adding a second story and new rooms, among them a striking glass conservatory (known as the garden room). A portico was added and the façade reworked. While the house is extensive—it has 21 rooms and measures 11,800 square feet—the architect reduced its mass by, among other means, setting its second story back away from the façade. “We tried to keep the one-story look.”

Although the couple initially planned to divide their efforts—he would oversee the exterior design, she the interior one—“I quickly lost my position,” the wife concedes with a laugh. Still, it was she who, when looking for an interior designer, summoned up the magic words: “Dorothy Draper.” A phone call to the late designer’s offices brought her into the orbit of yet another legend, Varney himself, who joined the firm toward the end of Draper’s tenure, in 1960. “He was perfectly charming,” the wife remembers. And quickly hired.

Dorothy Draper “stood art, nature, history, and geography on their ears when necessary in order to obtain from them her special personal refreshing effects,” the journalist Janet Flanner once wrote. Here, as so often, Varney does the same, mixing colors and styles just as boldly as his mentor once did.

The raw ingredients included a lifetime of disparate collections, from modernist paintings by the Czech artist Ernst Spitz, who’s one of the wife’s relatives, to such miscellany as textiles created by the couple’s daughter. “It’s all the threads of their life come together,” Varney says. “The clients wanted me to use everything they had.” A framed piece of needlepoint—a muted yet colorful family heirloom from long-ago Czechoslovakia—set the design wheels in motion; much of this residence has, like that artifact, a handworked, almost folkloric feel.

The expansive entrance hall is a case in point. A tapestry at the top of the stairway, visible upon entering, encapsulates both the residence’s palette and its handcrafted aesthetic. Every detail here, from the three-color floor, stenciled in a geometric pattern, to the hand-loomed runner on the curved staircase, is superbly crafted. The glass finial at the foot of the stairs is a vestige of old New England. “They always put a little piece of whalebone or tusk ivory on the end of the newel post to indicate that the mortgage was paid off,” explains Varney, who worked on the house with an associate, Laura Montalban.

In the adjoining living room, a gentle exoticism prevails. “Asian things work so well, whether they’re contemporary or traditional,” Varney says. The red-lacquered pagodas, set on either side of a sequence of French doors, are ready examples. The room’s distinctly outdoorsy feel is the result of some subtle sleight of hand. The square-patterned carpet, outlined in white, is reminiscent of paving stones; the soft palette and complex textures (including pale yellow walls—glazed, appliquéd and stenciled, as in almost every room here—and matching sofas of rich green brocade) conjure up a garden in spring. Floral accents, found on a wall hanging, sofa cushions and more, cheerfully perpetuate this illusion. Such mixed floral touches are very much a Draper signature. “Does the flower garden have only one flower and one or two colors? Absolutely not!” Varney has written.

The palette was the result of a gentle tug-of-war between the husband, who loves intense shades, and the wife, who prefers what she calls a “colorless” look. (Varney remembers her saying, “If it were left to me, everything would be cream.”) “Their collection really dictated the color scheme,” says Montalban. In fine Draper tradition, the colors can vary, sometimes radically, from one room to the next.

The master bedroom was brilliantly conceived in pale peach and blue gray. It’s a tranquil space with more than a touch of glamour to it. As elsewhere in the house, the designers reworked some of the couple’s existing furniture—here, century-old pieces of mahogany that once belonged to the wife’s parents. “Carleton said, ‘I’m making it Hollywood,’” the wife recalls, before having them refinished in a seductive, powdery bluish gray. Classic Dorothy Draper chairs, upholstered in an apricot-and-white check, “are the most comfortable ones in the house,” she adds.

Now that the project is complete, Varney’s clients look back in wonder. “He mixes colors that don’t go together!” the husband says, sounding almost incredulous and singling out one of the guest rooms—done in pale green and lilac, with accents of yellow, pink and white—as an example. “It works because Carleton makes it work.” The designer, serenely, invokes his fearless mentor. “Dorothy said, ‘If it looks right, it is right.’” He once wrote of this designer that “she could make it all work.” What he neglected to mention, and what he handily demonstrates here, is that he can, too.